Question

$y = 2x - 5$
$y = -x + 1$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Identify intercepts for $y=2x-5$

Y-intercept: when $x=0$, $y=2(0)-5=-5$ → point $(0, -5)$.
X-intercept: when $y=0$, $0=2x-5$ → $x=\frac{5}{2}=2.5$ → point $(2.5, 0)$.

Step2: Identify intercepts for $y=-x+1$

Y-intercept: when $x=0$, $y=-0+1=1$ → point $(0, 1)$.
X-intercept: when $y=0$, $0=-x+1$ → $x=1$ → point $(1, 0)$.

Step3: Verify intersection (optional check)

Set $2x-5=-x+1$ → $3x=6$ → $x=2$. Substitute $x=2$: $y=2(2)-5=-1$ → intersection $(2, -1)$.

Answer:

The line $y=2x-5$ passes through $(0, -5)$ and $(2.5, 0)$ (and intersects the other line at $(2, -1)$).
The line $y=-x+1$ passes through $(0, 1)$ and $(1, 0)$ (and intersects the other line at $(2, -1)$).
The graph provided correctly plots both lines with these key points.